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2 x 4 is the "rough cut" dimension. After that cut has been made the timber is planed down to 1 1/2 x 3 1/2 for "normal" timber. Kiln dried 2 x 4's are a fraction smaller.

Being European, you mentioned the reason I really screwed-up the first design job I did in the US, I had to re-do the drawings for the framing, soffits etc. Fortunately someone pointed it out to me before the building started.

I've seen 2x4's vary in size on the same stack from the yard,from 1 3/8 to1 5/8 and 3 3/8to3 5/8.
I usually go with 1 9/16 x 3 9/16 when adding them together.

This is rough lumber designed for framing and made to be covered by another surface,usually has a high moisture content,(in the winter you get it delivered covered with ice),so if you use it for critical projects inside when it dries out it is going to twist,warp,crack and check.

You can either leave it inside for a week or two then plane and joint it if you have access to these machines,or by #2pine of the same dimension,it is dried and surfaced to exact dimensions.
Pine is sold in 1/4s-a 2x4 would be 8/4x4.

Rough lumber(usually) is milled to the 1/2 ie:2x4&2x6=1 1/2x3 1/2 and1 1/2x5 1/2 until you get to 2x8-2x12 then its milled to the 1/4-1 1/2x7 1/4ect.

Man thats enough of that I'm starting to feel like I'm at work(anybody got an asprin my heads startin to kill me)